Question

If * is defined on R* as a * b = —ab/ 2,' then identity element in the group (R*., *) is *

Answer 1

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* is defined on R* as a * b = —ab/ 2

Let e be the identity element

Then a * e = e * a = a

Now

a*e =a gives

$- \frac{ae }{2} = a$

$\therefore \: e \: = - 2$

So - 2 is the identity element

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